Entropy on Riemann surfaces and the Jacobians of finite covers

Abstract

This paper characterizes those pseudo-Anosov mappings whose entropy can be detected homologically by taking a limit over finite covers. The proof is via complex-analytic methods. The same methods show the natural map ${\mathcal{M}}_g\to \prod {\mathcal{A}}_h$, which sends a Riemann surface to the Jacobians of all of its finite covers, is a contraction in most directions.